Method and apparatus for determining line sag in a conductor span

ABSTRACT

A method and apparatus for calculating line sag in a span of a conductor is provided. The method includes using a portable smart device having one or more accelerometers and running a line sag application on the processing device. The line sag application enables acceleration data of return waves generated on the conductor to be collected using the smart device and to be plotted as a function of time for display on the smart device. The method further includes placement of time markers on the plotted data displayed on the smart device to determine elapsed time and calculating line sag using the elapsed time.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority from U.S. Provisional PatentApplication No. 62/651,481 filed on Apr. 2, 2018 and Canadian PatentApplication No. 2,999,575 filed on Mar. 28, 2018 both entitled, “Methodand Apparatus for Determining Line Sag in a Conductor Span”. Entiretiesof the applications identified in this section are incorporated hereinby reference.

TECHNICAL FIELD

This disclosure relates to the field of power line construction,maintenance and services, and in particular to the determination of theamount of line sag in a power line conductor span.

BACKGROUND

It is known in the prior art to calculate the line sag of a conductorusing the time it takes for a travelling wave to travel along and returnfrom one end to the other of a conductor span. U.S. Pat. No. 5,454,272to Miller et al. requires mounting an impactor and at least one, andpreferably two, motion sensors mounted on the conductor being impactedby the impactor. The impactor causes a travelling wave along theconductor. The motion sensors detect the wave amplitude and timing.

Miller discusses a mathematical formula, described as being known in theart, for the calculation of the line sag. The calculated line sag isproportional to the square of the wave travel time. Miller disclosesthat the travelling wave can be caused by pulling down on the conductorand recording the return travel time.

IEEE Standard 524-2003, published 12 Mar. 2004, and entitled “IEEE Guideto the Installation of Overhead Line Conductors”, at page 62 describes:The stopwatch or sagwatch method is a quick and accurate means ofchecking sag. This method involves jerking or striking the conductor andmeasuring the time it takes the shock wave to be reflected back to theinitial point. Usually, three or five return waves provide an accuratemeasurement of the tension in the span. This method is most effective onsmall conductors and shorter spans. This method is also sometimesdifficult on lines with long unbraced horizontal post insulators becausethe insulators may absorb too much wave energy and make it difficult todetect multiple return waves.

Quanta Energized Services provides a training manual for linemen inbarehand procedures. The manual dated Jul. 10, 2015 and entitled“Barehand Training Manual” in Appendix A2, page 66 describes line sagmeasurement by using a stopwatch. The manual states that the return wavemethod of checking the sag in a conductor is applicable regardless ofthe span length, tension, size, or type of conductor, and that the timerequired for a wave initiated on a conductor, suspended in air betweentwo fixed supports, to traverse between the supports is dependent on theamount of conductor sag. The manual states that a conductor waveoriginating at one support will travel to the next support where it willbe reflected back to the point of origin where it will again bereflected back to the adjacent support, and that the cycle repeats untilthe wave is eventually damped out.

The manual describes striking the conductor with a blow close to onesupport point (approximately 8 feet to 12 feet from the support point)and simultaneously starting the stopwatch. Striking the conductor isdescribed as causing a wave to travel from the near support to the farone, where it is reflected. The manual instructs that at the thirdreturn of the wave, stopping the stopwatch and reading the time, inseconds, required for the wave to travel out and back three times. Therelationship between the time required for a conductor wave to travelthree times between supports and the conductor's sag is described asbeing given by the equation: Sag (in feet) equals the time (in seconds)squared, divided by 9.

This method is described in the manual as particularly valuable forchecking sag in spans of normal length, and as not being as satisfactorywhen used on very large conductors in long spans because of the greaterenergy required to set up a wave which can readily be felt after it hastraveled from one support to the other, three times.

The manual further describes that on a “hot” (i.e., energized) line theimpulse can be given and felt by means of a dry tested rope thrown overthe conductor 8 feet to 12 feet from the point of support.

Thus, for example, three return waves timed at collectively 9.24 secondsin a 613 foot span of 4/0 ACSR at 0.29 pounds per foot. Applying theformula: the collective 9.24 seconds was squared and then divided bynine. The result was 9.49 feet of sag in the span. An inaccuracy in atime measurement resulting in a measurement of, for example, 10.0seconds becomes a predicted sag of 11.1 feet, i.e., 1.6 feet more thanthe actual sag, an inaccuracy of 17 percent. Hence, both sensitivity tothe impulse of a returning wave and accuracy of time measurement isdesirable in order to consistently obtain accurate line sag measurement.

Applicant is also aware of U.S. Pat. No. 9,464,949 to Mahlen et al.entitled “Wire Timing and Tensioning Device”, the entirety of which isincorporated herein by reference. Mahlen describes his method, deviceand system as being semi-automated. The device is attached to atensioned line and is used to measure a total time delay of an inducedmechanical wave in the tensioned line. The total time delay is thencompared to a sag-tension chart by a user to determine the line sag.

SUMMARY

Accordingly, in one broad aspect, a method for calculating line sag in apower line suspended between at least two supports is provided. Themethod comprises providing a smart device having an accelerometer, adisplay, an user interface, a processor, a memory, and at least oneapplication residing in the memory. The method further comprisestemporarily coupling the smart device to the power line and launchingthe at least one resident application. Further, a mechanical wave isinduced on the power line by pulling the smart device, while coupled tothe power line, in a substantially vertical direction. The mechanicalwave generates a plurality of return waves in the power line.Acceleration of a subset of the plurality of return waves andcorresponding vertical acceleration of the smart device is recorded.Each return wave of the subset of return waves has multiple, and thesame number of harmonics. Timings of the subset of return waves arerecorded. Within the at least one resident application, and using therecorded acceleration and timings, a graphical waveform representationof the subset of return waves is generated and the graphical waveformrepresentation is displayed on the display. Using the user interface,the displayed graphical waveform representation is magnified so as toview the harmonics of each of the subset of return waves. A harmonic ofa first return wave of the subset of return waves is selected and usingthe user interface a start marker is placed on a displayed inflection(for example, a peak or valley) of the selected harmonic of the firstreturn wave. A harmonic of a second return wave of the subset of returnwaves is selected and, using the user interface, a stop marker is placedon a corresponding inflection of the corresponding selected harmonic ofthe second return wave. Then, within the resident application, a timedelay is calculated between the start marker and the stop marker, andthe line sag is calculated using the time delay.

Accordingly, in another broad aspect, a portable, modular system forcalculating line sag in a power line suspended between at least twosupports is provided. The system comprises a smart device including anaccelerometer, a display and an user interface. The system furthercomprises a coupler for temporarily coupling the smart device to thepower line; and at least one executable application resident or adaptedto be resident in the smart device. The application, in operation,performs the following steps: records acceleration of a subset of aplurality of return waves generated in the power line and correspondingvertical acceleration of the smart device when coupled to the powerline; records timings of the subset of return waves; generates agraphical waveform representation of the subset of return waves usingthe recorded acceleration and timings and displays it on the display.Each return wave of the subset of return waves has multiple, and thesame number of harmonics. The application also calculates a time delaybetween a start marker and a stop marker placed on inflections (forexample, peaks or valleys) of selected corresponding harmonics of thesubset of return waves; and calculates the line sag using the timedelay. The amount of the calculated line sag is then displayed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is an illustration of one embodiment of a method for calculatingline sag in a power line, FIG. 1A shows coupling of a smart device tothe power line by a user;

FIG. 1B illustrates launching of an application resident on the smartdevice of FIG. 1A by the user;

FIG. 2A illustrates the user pulling the smart device to induce amechanical wave in the power line;

FIG. 2B illustrates a screen of the smart device of FIG. 1A displayingaspects of the application after the same has been launched;

FIG. 3 illustrates the user holding onto the smart device of FIG. 1A forrecording acceleration and timing of a subset of return waves generatedby the mechanical wave;

FIG. 4 depicts a graphical waveform representation of the inducedmechanical wave and the subset of return waves as displayed on thescreen of the smart device of FIG. 1A;

FIG. 5 illustrates placement of a start marker and stop marker on thegraphical waveform representation of FIG. 4 by the user;

FIG. 6 illustrates wave grouping or harmonics of a first return wave;and

FIG. 7 illustrates wave grouping or harmonics of a second return wave.

DETAILED DESCRIPTION

The presently disclosed application and its method of use which resultsin a calculation of line sag in a conductor takes advantage of thepresence of accelerometers in portable or hand-held electronics such ascell phones or so-called smart phones or small tablet computers or othersmart devices and the like (herein also referred to as a “hand-heldprocessing device” or “device”, or alternatively as a “phone”).

As used herein, the term “tablet”, “smart phone”, “smartphone platform”,“smart device” or “smart phone-type device/system” means a mobileapparatus that is capable of running a programmed application suitablefor executing the embodied functionality. While suitable traditionalsmart phones and tablets may include products such as, e.g., theiPhone™, iPad™ which are products of Apple, Inc.™, Android-baseddevices, and other commercially available devices and associatedoperating systems, the term “smart device” as discussed and embodiedherein is intended to include any digital mobile device such as smartphones, tablets, phablets, smart watches, and other current or future“smart phone” platforms having similar functionality. In order to beespecially useful and convenient, in one preferred embodiment the smartdevice is relatively small, so as to fit in a clothing pocket forexample, and thus does not have an overly large display screen. Wherethe display screen is relatively small, for example a few inches, or upto five inches, measured diagonally across the screen, it has been foundadvantageous if the screen is a touch sensitive screen and where thedevice operating system accepts zoom-in (magnify) and zoom-out commandsusing touch control so that a displayed graph and data on the graph maybe magnified to see data detail not otherwise easily seen by the user.

As will be understood by a person skilled in the art a smart device, inaddition to accelerometers and a display, typically includes a userinterface, a processor and a memory. The user interface advantageouslymay be a touch sensitive screen, or may include a keyboard, a mouse, ora button or buttons, but it is not limited thereto.

The accelerometers in the device interact with the display on the deviceso as to orient the display on the device for ease of viewing or readingno matter which way the device's display screen is oriented in avertical plane. The accelerometers use the acceleration due to gravityto detect a downwards direction and this information is used by thedevice's processor to orient the displayed data so that what is intendedto be downwards in the displayed image is in fact oriented downwardly onthe display's screen. Many conventional programs or applications runningin such hand-held processing devices use the accelerometer data. It isthus known to one skilled in the art when programming applications touse the accelerometer data for the purposes of orienting a display or,in game-play, for the detection of movement of the device which signalsinput from the user to interact with the game or other applications.

In the present disclosure a line sag application or “app” which isresident in the device memory uses the accelerometer data from theaccelerometers in the device for at least two purposes. Firstly, as isconventional, the accelerometers detect the downwards direction.Secondly, the accelerometers detect vertical acceleration due tofirstly, a downward force imparted manually to a conductor line or powerline at one end of a span, and, secondly, the impulses due to thereturning travelling waves in the conductor.

Thus, as seen in FIG. 1A, a user 10, who is standing on the groundgrasps a pulling rope 12 or other preferably dielectric pulling memberwhich has been suspended downwardly from one end of an over-headsupported conductor span or power line (not shown). With the hand-heldsmart device 14 coupled to the lower end of the rope, and with the linesag app (better described below) started by user 10 pushing the startbutton (labelled start) on the display 14 a as seen in FIG. 1B, the userpulls sharply down once on the rope 12. Advantageously, the upper end ofthe rope is affixed to the conductor about eight feet (approximatelythree meters) out along the conductor from the insulators suspending theconductor from the support structure, which may be a tower 16. In oneembodiment, the power line is suspended between two support structures.

The device 14 may be coupled to the rope 12 at a height on the ropeconvenient for the user 10. The coupling of the device to the rope 12may, as shown in FIG. 1A-3, be as simple as the user merely holding thedevice 14 against or adjacent to the rope 12 while simultaneouslyholding the rope 12 so that any vertical movement of the rope 12 alsosimultaneously moves the device 14 correspondingly vertically. Thedevice may also be temporarily mechanically coupled to the rope. Forexample, although not illustrated, the device may be held snugly in acase, sleeve or sheath and clipped, for example by a carabiner 12 a, oradhered, for example by hook-and-loop releasable fasteners, to the rope12. For the former, the rope 12 may have a loop formed in it, forexample located at approximately shoulder height relative to the user,to assist in coupling the device 14 to the rope 12 using the carabiner12 a. Other forms of releasable couplers will also work; for examplewhere one end of a coupling device, such as a male/female mating clip,is attached to the rope. The coupling device may be attached to the ropefor example by the use of a releasable clamp, or by tying or lashing tothe rope, or by a base mounted to the rope. With one end of the clipthus mounted to the rope and with the other end of the clip mounted tothe device, the device 14 may be releasably secured to the rope.

Whether or not employing a clip or otherwise securing the device 14 tothe rope 12, as seen in FIG. 1A the user 10 may stabilize the device 14against the rope by grasping the device 14 so as to pin or wedge itagainst the rope 12. With the device 14 thus temporarily anchored to therope by any of the above coupling means, and with the line sag appstarted as seen in FIG. 2B, the user 10 then pulls down on the rope 12in direction A (see FIG. 2A) to create or induce the initial impulse tothe conductor and corresponding initial wave acceleration 18 in theconductor.

The device 14 remains coupled to the rope 12 until a travelling wavegenerated by acceleration 18 has travelled along the conductor span andhas been reflected back, advantageously until two or more, andpreferably three return waves have been reflected back along theconductor to the user's position where the rope is connected to theconductor. As used herein, the end of conductor where user 10 is locatedis also referred to as the first end or wave generating end of theconductor. Each reflected wave as it returns along the conductor to thefirst end causes an upward kick or bump acceleration in the conductorbriefly lifting the rope 12 as it passes thereby causing an upwardacceleration of the device 14. The accelerometers in the device aresensitive and detect the upward acceleration caused by each bump,including even a small amplitude wave (e.g. the third returning wave).The corresponding accelerometer data is recorded and displayed by theapp as a plot of vertical acceleration over time to show the magnitudeof each returning wave as an acceleration profile over time, such asseen in herein by way of example in FIGS. 4-7.

Without intending to be limiting, using the illustrated example of thedevice 14 remaining coupled to rope 12 until acceleration data has beencaptured for a subset of return waves such as four returning waves, thedevice display 14 a in FIG. 4 shows a plot of the acceleration profileover time as detected by the accelerometers in device 14. The initialacceleration spike of the initial wave impulse 18 is shown at the leftside of the display 14 a. The initial acceleration spike is the resultof the user 10 pulling sharply downwardly on rope 12 as shown in FIG.2A. User 10 then waits for the return waves returning after beingreflected back toward the user along the conductor. Each returning waveis felt by the user 10 and the device 14 as an upward kick, bump or tugin direction B of rope 12. Thus in FIG. 4 the corresponding return waveprofiles 20, 22, 24, 26 for the first, second, third and fourth returnwaves respectively are shown sequentially from the left to the right onthe device display 14 a. In this example, time is recorded along axis Cso as to provide the time difference between the first and last of therecorded returning waves. The time difference is then used to calculatethe line sag in the corresponding conductor span.

Because, as described above, the line sag determination is proportionalto the square of the recorded elapsed time (i.e., line sag isproportional to elapsed time squared), the accuracy of reading the timeis important to the accuracy of the determination of the amount line sagin the span. Thus errors in the reading of the time are amplified as theamount of error in time recorded, is squared. In one aspect of thepresent method the accuracy is improved by the use of an accelerationprofile vs. time plot on the display. The illustrated accelerationprofiles are those of the returning waves; e.g. 20, 22, 24, 26. Eachreturning wave, when enlarged, is made up of a grouping of small wavesor harmonics. Each consecutive grouping of harmonics has a similaracceleration over time profile; with substantially only the waveamplitude of each subsequent grouping of harmonics decreasing as betweensubsequent profiles for the first, second, third, etc. returning wave.Thus the present method, in one aspect, which is not intended to belimiting, takes advantage of this tendency of each of the returningwaves to have a similar waveform profile which merely reduce inamplitude due to the damping of the wave energy with each successivereturning wave. The similar outline of these returning waveform profilesfor returning waves 20, 22, 24, 26 are seen in FIGS. 4 and 5, and asenlarged in FIGS. 6 and 7.

As seen in FIGS. 6 and 7, the displayed waveform of the returning waveshave been expanded or enlarged for ease of viewing of the harmonics ofthe returning waves, for example by using a conventional zoomingfunction on the device display 14 a. Where the device 14 is a touchscreen smart phone on some devices 14 zooming or expanding may be doneby figure gesture such as a two finger spreading motion on the displaytouch sensitive screen. Spreading the fingers while in contact with thetouch sensitive screen enlarges or zooms the display between the contactpoints of the fingers. A person skilled in the art will understand thatthe magnifying function may be achieved using user interfaces other thana touch sensitive screen, for example, a keyboard, a mouse, or a button,but it is not limited thereto. The user input via the user inputinterface may include a touch, a zoom-in, a zoom-out, or a swipeoperation using a touch sensitive screen, but it is not limited thereto.The user input via the user input interface may include a click, adouble click, or a drag and drop operation, but it is not limitedthereto, as other interface functions such as voice commands will alsowork.

As seen in the enlarged views of FIGS. 6 and 7, the waveforms of theharmonics of the returning waves have multiple adjacent peaks withineach wave's acceleration profile. For example, wave 26 has multipleharmonics having peaks 26 a-26 d as seen in FIG. 6, and wave 20 hascorresponding multiple harmonics having peaks 20 a-20 d as seen in FIG.7. The displayed timer function allows the user to first place astart-timer marker 28 on a peak of a chosen harmonic (e.g., the firstpeak 20 a) of the first returning wave 20 using the user interface whichin the embodiments described herein is a touch sensitive screen. Theuser then places a stop-timer marker 30 on a peak of a chosen harmonic(e.g., the first peak 26 a) of the fourth returning wave 26. The chosenharmonics (e.g. peaks 20 a, 26 a) on the first and fourth returningwaves have similar profiles. Thus placing the timer start and stopmarkers (which dictate the measured time increment there-between) oncorresponding harmonics, and in the same position on each harmonic,increases the accuracy of the time delay calculation. As explained inthe Background, accuracy of time measurement is an important aspect inobtaining an accurate line sag measurement because the line sag isproportional to the square of the time. Since the method describedherein enables the user to locate the markers on corresponding peaks of(or corresponding valleys between) harmonics that have the same profile,and the same relative position within each returning wave, accuracy oftime measurement is increased. Calculation of the time measurement isnot random but is intended to be between specific correspondingharmonics.

In example illustrated in FIGS. 4 to 7, the user 10 places a fingertip(not shown) on the balloon icon 28 a of the start-timer marker 28displayed on the touch screen display 14 a of the device 14 and slidesthe balloon icon laterally in direction D so as to place the start timermarker 28 on the peak (e.g., 20 a) of the desired harmonic of the firstreturning wave 20. Similarly, the user subsequently places a fingertipon the balloon icon 30 a of the stop-timer marker 30 as also displayedon the touchscreen display 14 a of the device 14 and slides the balloonicon 30 a laterally in a direction E so as to place the stop timermarker 30 on the peak 26 a of the corresponding harmonic of the fourthreturning wave 26 seen in FIG. 6. The placement of each marker 28, 30,is assisted by the user zooming in on or expanding the view of, orotherwise magnifying, firstly, the first returning wave 20 as seen inFIG. 7, and, secondly, the fourth returning wave 26. With both markers28, 30 placed on the desired corresponding peaks (e.g., 20 a, 26 arespectively) and with the plot 32 on display 14 a un-zoomed,un-expanded or un-magnified so that both markers 28, 30 can be seensimultaneously on the display as seen in FIG. 5, the time determinationstep is initiated. The time determination is the stop-timer marker 30reading (in seconds) minus the start-timer marker 28 reading. This isgenerated by the device processor. Since the start and stop markers areplaced on peaks of harmonics having the same profile, an accurate timingof the time elapsed is achieved. In the illustrated example in FIG. 5,the time determination is displayed as the time between markers 28, 30along axis C. As stated above, the markers 28, 30 may be set on othercorresponding peaks of earlier and later returning waves, other than thefirst and fourth returning wave, provided that the returning wave hassufficient amplitude so that its sequence of adjacent peaks may bedetected by the accelerometers. Advantageously, the sensitivity of theaccelerometers may be adjusted within the app; the example being shownin FIG. 1 of a default 0.3 g setting.

In one embodiment, the smart device in conjunction with the app mayallow the user, if the user so wishes, to re-position a marker. In oneembodiment, the user may need to first remove the marker, before zoomingin on a different portion of the graphical waveform representation andre-placing the marker. Thus the earlier position of the marker is lost.The user may be able to use different zoom levels to gradually “home in”on the point on the graphical waveform representation which the userwishes to mark. As described above, such zoom control interfaces areknown in the art.

In one embodiment, the start and stop markers are insertion markers suchas a cursor, an insertion bar, an insertion point, or a pointer.

As explained above, the user uses the touch screen of the device to zoomin on the return waves displayed on the device's screen, which, uponenlargement, show that each return wave is a grouping of small waves orharmonics.

In one embodiment, the user uses a pair of horizontally slidableinsertion markers (see FIG. 5) to mark where the elapsed time on thegraph is to be measured from and where the timing is to be stopped. Inone embodiment, the markers each have a finger button such as a balloonicon for the user to hold the tip of the user's finger against, whichthen allows the user to slide each marker back and forth on the touchscreen, horizontally along the elapsed time axis, using a light fingerpressure on the marker button. With the first return wave enlarged so asto show it's harmonics (as seen in FIG. 7), the user slides the markeronto the top of a peak of one of the harmonics, say the first one. Thatflagged harmonic then becomes where the timing starts. The user thenshifts over to, and zooms in on the fourth return wave on the graph. Theuser then slides the second marker onto the same harmonic (in the caseof this example, the first harmonic) on the fourth return wave as wasused to mark the first return wave. See FIG. 6. With this done, theelapsed time for the line sag formula is accurately now the exact timebetween the two marked harmonics. All of this is done conveniently onthe job site, in fact without the user necessarily even moving fromunder the power line, and is completed within minutes by the user.Again, the exactness of the measured time between the correspondingharmonics in the returning waves as determined by the placement of thestart and stop timing markers provides exactness in the calculated linesag because errors in the timing measurement are squared, resulting incorrespondingly larger errors in the calculated line sag.

What is claimed is:
 1. A method for calculating line sag in a power linesuspended between at least two supports, the method comprising:providing a smart device having an accelerometer, a display, a userinterface, a processor, a memory, and at least one resident applicationresiding in the memory; temporarily coupling the smart device to thepower line; launching the at least one resident application; inducing amechanical wave on the power line so that the mechanical wave generatesa plurality of return waves in the power line; using the at least oneresident application, recording acceleration of a subset of theplurality of return waves and corresponding vertical acceleration of thesmart device, wherein a first return wave of the subset has a firstnumber of harmonics and wherein a subsequent second return wave of thesubset has a second number of harmonics, and wherein the first number ofharmonics is equal to the second number of harmonics; recording timingsof the subset of the plurality of return waves; within the at least oneresident application, and using the recorded acceleration and timings,generation a graphical waveform representation of the subset of theplurality of return waves and displaying the graphical waveformrepresentation on the display; using the user interface to magnify thedisplayed graphical waveform representation so as to view the harmonicsof each of the subset of return waves; selecting a harmonic of a firstreturn wave of the subset of the plurality of return waves and using theuser interface to place a start marker on a displayed inflection of theselected harmonic of the first return wave; selecting a harmonic of asecond return wave of the subset of the plurality of return waves and,using the user interface, placing a stop marker on a correspondinginflection of the corresponding selected harmonic of the second returnwave; within the resident application: calculating a time delay betweenthe start marker and the stop marker, and calculating the line sag usingthe time delay.
 2. The method of claim 1, wherein the smart device is asmart phone having a touch sensitive screen and the magnifying stepincludes a multi-fingered swipe gesture on the touch sensitive screen.3. The method of claim 2, wherein the inflection is a peak and the stepof placing the start and stop markers includes tapping a region of thepeak of the selected harmonic for placement of an insertion marker onthe peak.
 4. The method of claim 2, wherein the inflection is a peak andthe step of placing the start and stop markers includes touching andholding an insertion marker displayed on the screen and subsequentlymoving the insertion marker to the peaks of the selected harmonics forlocation thereon as the start and stop markers.
 5. The method of claim4, wherein the step of moving includes a sliding finger gesture on thetouch sensitive screen.
 6. The method of claim 1, wherein the start andstop markers are insertion markers chosen from the group comprising acursor, an insertion bar, an insertion point, a pointer.
 7. The methodof claim 1, wherein the step of coupling includes encasing the smartdevice in a sheath and releasably connecting the encased smart device toan end of a dielectric pulling member suspended downwardly from thepower line.
 8. A portable, modular system for calculating line sag in apower line suspended between at least two supports, the systemcomprising: a smart device including an accelerometer, a display and auser interface; a coupler for temporarily coupling the smart device tothe power line; at least one executable application resident in thesmart device that, in operation, performs the following steps: recordsacceleration of a subset of a plurality of return waves generated in thepower line and corresponding vertical acceleration of the smart device;records timings of the subset of return waves; generates a graphicalwaveform representation of the subset of return waves using the recordedacceleration and timings and displays the graphical waveformrepresentation on the display, wherein a first return wave of the subsethas a first number of harmonics and wherein a subsequent second returnwave of the subset has a second number of harmonics, and wherein thefirst number of harmonics is equal to the second number of harmonics;provides means for: using the user interface to magnify the displayedgraphical waveform representation so as to view the harmonics of each ofthe subset of return waves; selecting a harmonic of a first return waveof the subset of the plurality of return waves and using the userinterface to place a start marker on a displayed inflection of theselected harmonic of the first return wave; selecting a harmonic of asecond return wave of the subset of the plurality of return waves and,using the user interface, placing a stop marker on a correspondinginflection of the corresponding selected harmonic of the second returnwave; calculates a time delay between the start marker and the stopmarker; and calculates the line sag using the time delay.
 9. The systemof claim 8, wherein the smart device is a smart phone and the userinterface is a touch sensitive screen of the smart phone.
 10. The systemof claim 8, wherein the coupler includes a dielectric pulling memberadapted to be suspended downwardly from the power line and at least acarabiner to releasably couple the smart device to a free end of thedielectric pulling member.